Newest version of (Video) Download Helper does not have the drop-down arrow on the toolbar icon but does have the drop-down arrow next to the icon at the bottom of the Firefox window:
*Firefox 3 it is in the Status Bar
*Firefox 4 and later it is in the Add-on Bar
To display:
*Firefox 3 Status Bar: View > Status Bar must be checked
*Firefox 4 and later: Firefox button > Options > Add-on Bar must be checked

Question owner

This answer still left me confused. Finally I found that the "show in status bar" was unchecked in Preferences/General/ Appearance. After checking that box I had the icon @ the bottom & was back on the road again.
I'm sure it would help if then next time something was moved from the top to the bottom of the page a little notification would help. The Downloader Helper instruction manual still tells you the triangle is up top next to that icon.

This answer still left me confused. Finally I found that the "show in status bar" was unchecked in Preferences/General/ Appearance. After checking that box I had the icon @ the bottom & was back on the road again.
I'm sure it would help if then next time something was moved from the top to the bottom of the page a little notification would help. The Downloader Helper instruction manual still tells you the triangle is up top next to that icon.

After posting the above, was mentioned elsewhere that the developer had posted a new, not reviewed (by Mozilla) version that restores the arrow to the toolbar icon. I do not know if it was
*because of complaints and the developer intentionally omitted the drop-down arrow previously, or,
*if in the previous code the developer just made a mistake in omitting the drop-down arrow
If you want to try the new, not reviewed version, you can install version 4.9.2 from the following link:
*https://addons.mozilla.org/en-US/firefox/addon/video-downloadhelper/versions/

No idea why DownloadHelper would change it's default interface after so many years.
Here is how you get the "download menu" back when you click on the DownloadHelper icon in the toolbar:
Tools > DownloadHelper > Preferences > General > Behavior Tab
1) Check - Extended Download Menu
2) Change dropdown to - Open Menu